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http://dx.doi.org/10.5351/KJAS.2016.29.7.1165

An optimal management policy for the surplus process with investments  

Lim, Se-Jin (Department of Statistics, Sookmyung Women's University)
Choi, Seungkyoung (Department of Statistics, Sookmyung Women's University)
Lee, Eui-Yong (Department of Statistics, Sookmyung Women's University)
Publication Information
The Korean Journal of Applied Statistics / v.29, no.7, 2016 , pp. 1165-1172 More about this Journal
Abstract
In this paper, a surplus process with investments is introduced. Whenever the level of the surplus reaches a target value V > 0, amount S($0{\leq}S{\leq}V$) is invested into other business. After assigning three costs to the surplus process, a reward per unit amount of the investment, a penalty of the surplus being empty and the keeping (opportunity) cost per unit amount of the surplus per unit time, we obtain the long-run average cost per unit time to manage the surplus. We prove that there exists a unique value of S minimizing the long-run average cost per unit time for a given value of V, and also that there exists a unique value of V minimizing the long-run average cost per unit time for a given value of S. These two facts show that an optimal investment policy of the surplus exists when we manage the surplus in the long-run.
Keywords
surplus process; martingale; optional sampling theorem; renewal reward process; optimal investment policy;
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Times Cited By KSCI : 1  (Citation Analysis)
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